Wednesday, March 25, 2015

Housing Tax Policy, A Series: Part 23 - Rent Inflation and Home Prices

Yesterday, I touched on the relationship between rent inflation and home price inflation.  Owner equivalent rent inflation has been above core inflation for 30 years and rent inflation in general has been higher than core inflation for 15 years.  I have made the point before that this is a very odd finding if we just saw a period of over building.  It's also an odd finding if the steep rise in mortgage debt was a product of median household desperation and stagnation.

Here is a graph of shelter inflation, core inflation, and the homeownership rate.  I would say that the general rate of inflation is a reflection of monetary policy.  The relative rate of shelter inflation is a reflection of tax policy, other public policies, and market trends which increase or decrease relative demand for housing.  The relative level of shelter inflation was low, briefly, in 1976, 1983, and 2010.  But, generally friendly policies and financial developments led to increased demand for owner-occupied housing in the late 1960s, late 1970, mid 1980s, 1990s, and 2000s.  These periods usually correspond to rising homeownership rates.  The high shelter inflation since 2007 has corresponded with sharply dropping homeownership rates.  As I showed yesterday, shelter inflation before this period came from owner equivalent rent, but this recent period has seen a rise in tenant inflation.  Earlier shelter inflation came from a shift right in owner-occupier demand, but this inflation is coming from a shift left in supply.  The shift in supply comes from the credit market, so the recent rise in rent inflation has been associated with very low home prices.  There is demand for housing, but there is no source of funds for it to be expressed in the owner-occupier market.

In any case, the direct relationship between rent and price only gets us so far.  Even using the Price/Rent ratio, home prices have risen from the mid 1990s levels by 47% to 100%, depending on the measure we use, and are from 22% to 68% higher than the previous high points seen in the late 1980s.

But, I think there is a more subtle interaction between rent inflation and home prices that has to do with homes as a financial security.  If we think of home ownership simply as a perpetual bond, which takes as its coupon payments the net rent on a particular house (after maintenance, taxes, and depreciation), a house is similar to a TIPS bond.  But, the inflation adjustment on a TIPS bond is based on the CPI.  On a home, the inflation adjustment is based on the specific local real estate market.

I think the required return of both homes and TIPS bonds begins at a level that reflects arbitrage with other investment alternatives.  With TIPS, this is relatively straightforward.  We can begin with the interest rate on nominal bonds and subtract expected inflation.  We usually go the other direction.  Since there is a market price for both TIPS and nominal bonds, we can infer expected inflation from the difference.

The sharp difference in real rates from 1978-1986 stems from the
sharp changes in inflation expectations, and the lack of a good
way to measure the effects of this on different durations. 
I submit that home prices operate in much the same way.  We begin with the nominal interest rate on very long term bonds, and we subtract expected inflation.  But, instead of inflation coming from the CPI, inflation comes from the specific expectation of nominal rent levels at that specific location.  This means that in areas where rent is expected to rise - growing cities, gentrifying neighborhoods, etc. - we should expect to see price/rent ratios much higher than average, because these homes will have a larger inflation discount.  And since all homes, no matter where they are located, should tend to provide the same expected present value of cash flows, the additional inflation discount on homes with higher expected future rents should lead to higher prices relative to the current rent.

Over time, I find that returns on homes, in the aggregate, do tend toward that non-arbitrage return level, relative to bonds.  Because they are perpetuities, there is much less cyclical fluctuation in home returns.  Also, they tend to have a premium (from liquidity, duration, and other complications of ownership) of about 1.5% compared to cyclically adjusted real 10 year treasury rates.

Comparing the nominal yield of 30 year mortgages to the real, implied yield of home ownership, we can perform the same inflation inference that we do with TIPS.  And, this measure produces an inflation premium very similar to the premium we see in TIPS and a real rate of return similar to what we see in cyclically adjusted real bonds, confirming that non-arbitrage pricing is effective in the housing market. (The real return on homes probably is approx. 0.5% higher than the real 30 year mortgage rate, because of the higher duration of the home, so this causes the inflation premium implied by mortgages and home returns to be understated by about 0.5%.)

The housing market has not been in equilibrium since 2007 (in other words, homes provide excess profit compared to fixed income alternatives - see the graph above with the output gap), so the inflation premium cannot currently be estimated in the housing market.  Even though real interest rates were low in the late 1970s, I originally thought that the high inflation rates must have dampened effective demand for housing by making mortgages unaffordable, which would depress Price/Rent (increase real returns).  But, real returns on homes did fall below 3% during that time, and the implied inflation premium is about where we would expect it to be for that period.  As I have looked at the data, it has begun to look as if low real interest rates were still incentivizing households into homeownership.  The homeownership rate rose in the late 1970's, and shelter inflation was strong.  But, imputed rent was falling as a portion of GDI until the Volker recession in 1980.  It looks as though households were moving into owner-occupied homes, but prices remained at the approximate no-arbitrage levels.  Normally, households would increase their housing consumption when they buy a home, because of the tax advantages of owning.  In the late 1970s, high mortgage payments were the obstacle to those excess gains, so marginal households had to downsize to capture it.  We can see in this graph that the average home price moved up relative to the marginal home price.  This downward shift for marginal home buyers created a positive skew in the homebuyer market, causing this shift.  (This may be a sort of just-so story, but I think that the market would have readjusted back to a less skewed market.  But beginning with the mortgage deduction in 1986, high income households were incentivized to consume more housing.  So, as nominal mortgage rates declined, marginal owner households consumed more shelter, but higher income households also consumed more shelter because of the mortgage tax deduction.)

Implications for Case-Shiller Home Price Indexes

I'm getting off track here.  The point of this post is that localized home prices, in theory, should be related to the local expectations of rent inflation, which could come from local development, zoning limits, or other local sources of shelter demand or obstacles to shelter supply.  As I laid out in yesterday's post, rent inflation has been higher in the 10 cities included in the Case-Shiller 10 city index than it has been in the rest of the country.  So, this would naturally cause prices to rise in proportion.  But, what I am describing in this post is a more subtle effect.  Persistently higher localized rent inflation would also increase the equilibrium Price/Rent level.  And, this is what we see in the indexes.

From 1985 to 2013, core CPI inflation averaged 2.8%, national Owner Equivalent Rent for Primary Residences averaged 3.2%, and OE Rent for Primary Residences in the 8 cities that have CPI measures from the Case-Shiller 10 city index averaged 3.5%.

So, simply using the rent level, the YOY rent inflation, and a very long term mortgage interest rate, implied from 15 year and 30 year mortgage rates (which ranges from 0.3% to 0.9% higher than the 30 year mortgage rate, depending on the steepness of the yield curve), I have a simple model of expected home prices to compare to actual prices.  Here, I am using the Case-Shiller indexes, so I have simply calibrated the modeled prices to roughly match the Case-Shiller indexes in the 1993-1994 time period.

I use the rent levels specific to the index (national OE rent for the National Index and average OE rent for 8 of the 10 cities in the 10-City Index).  I am simply using the rent inflation rate for a given year as my inflation rate adjustment.  In order to minimize noise from single-year rent inflation fluctuations, I have limited home price increases to a maximum of 15% per year.  I am valuing the homes as perpetuities, so the formula is very simple:
(CPI Rent Level) / (Estimated very long term Nominal Mortgage Rate - YOY Rent Inflation) * Constant
Here is a graph of the modeled prices corresponding to the National Index and to the 10-City Index.

At current interest rates, modeled home prices would be much higher, but they are limited by the 15% maximum gain.  In order for the modeled prices to fall back to today's market prices, long term real rates would need to rise by about 2%, which is about where they were in the late 1990's and at the high point in 2006-2007.  Long term rates are less volatile than short term rates.  It would be unlikely for long term rates to rise that high unless the Fed Funds Rate rises above 4%.

A reasonable scenario where the Fed Funds Rate rises to 3-4% by, say, early 2017, with nominal 10 year treasuries at 4% and 30 year mortgages at 5.5%, with typical 2.5% implied expected inflation, would put mature recovery home prices a little bit above where they are now - may 10-15% higher - with real implied returns on home ownership of 3-3.5%.  But, if the natural level of interest rates at full recovery rate levels ends up lower than that, there might be more room for home prices to rise before they settle in to a more typical, inflation level rate of annual appreciation.

A couple of implications from this projection:
1) Fed Funds forward prices are currently less than 1.5% in early 2017.  I wonder if there is a good hedged position to be taken here by pairing a short Eurodollar or Fed Funds contract with some sort of position that has long exposure to home prices.

2) Since long term real interest rates have been low and volatile, and since the effect of low real long term interest rates on durable real assets becomes stronger at lower rates because of the convex relationship between rates and asset prices, I think it would be much safer in this context to target 2-4% inflation instead of 1-2% inflation we have seen since the turn of the century.  Even in the early 1990's, Price to Rent levels declined by around 20% over a number of years.  Since inflation was around 4-5% at the time, nominal home prices remained stable and we avoided a mortgage crisis.  Eventually, secular real rates will rise.  A slightly higher inflation rate will probably create more stability when they do.

Higher inflation might dampen home demand slightly because of the higher mortgage payments that are required in a higher inflation context.  But, the inflation premium itself may create more stability than any dampened demand does.  Because, as I have outlined, since mortgages are a nominal security and homes are a real security, the inflation premium portion of the mortgage interest expense is really a pre-arranged purchase of home equity by the owner, from the lender.  In effect, because of our current conventions in home buying, higher inflation forces home buyers to increase their real equity positions in their homes at a faster pace.


  1. Interesting article in the Economist on housing & inequality:

    Your series on housing appear to be making similar arguments: that homeowners are grabbing an outsized share of the pie. Care to comment?

    1. Thanks for the link, Joe. I think I'll add this to a short list of comments which I need to reply to in full posts. This issue is so complicated.

  2. This comment has been removed by the author.

  3. Another link to a similar paper on housing and inequality.

    Chuck E.

    1. Thanks Chuck. This will be in an upcoming post.